Generalizing the results of the previous section, one can show (see again [1]} for details) that the set of dominant schemes with degree \(\delta \)  and \(r\)  roots, \( {\cal S}^{\text{dom}}_{\delta , r}\) , consists in binary trees with \(r\)  univalent root vertices and another \(2\delta \)  univalent vertices. Such trees have \(2\delta + r -2\)  three valent internal vertices and \( 4\delta + 2r - 3\)  edges. The leading singular contribution to the \(2r\) -point function is then
\(\mathfrak {K}^{(1)\text{sing}}_{2r} = N^{3(1-r)} \sum _{\delta \in \mathbb {N}/ 2} N^{ - \delta }\sum _{S \in {\cal S}^{\text{dom}}_{\delta , r} }T\big (\lambda ^2\big )^r \big [2^2 U\big (\lambda ^2\big ) \big ]^{\delta } \big [1+3 U\big (\lambda ^2\big )\big ]^{2\delta +r-2} \nonumber \\\hphantom{\mathfrak {K}^{(1)\text{sing}}_{2r} =}{} \times \left( \frac{6 [ U(\lambda ^2)]^{ 2 } }{ [1-U(\lambda ^2) ] [1-3U(\lambda ^2)] } \right)^{4\delta + 2r-3} ,\) 
